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In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe...

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Physics

In winter, people play hockey on Alta Lake in Whistler.However, it is not considered safe by the Canadian Red Cross toplay hockey on ice until the ice is 20 cm thick. On a winter daywith a temperature −10◦C, it is observed that the lake has a 1cmthick layer of ice over the entire surface.
Constants which may be of use: The thermal conductivity of iceis 2.18W/m · K. Density of ice 916.7 kg/m3 and water 1000 kg/m3.Latent heat of fusion 334x103 J/kg.

a) If the air temperature remains at −10◦C, find the rate incm per hour at which ice is added to the layer initially. Thethermal conductivity of ice is 2.18W/m · K. Answer in cm/hour. Theunits are already written for you.

b) Find the rate in cm per hour at which ice is added to thelayer as a function of the thickness X, where X is the number ofcentimeters.

c) Estimate the time it takes before you can safely playhockey

Answers: a) 2.56 cm/hr b) 2.56/X c) 3 days

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